Primitivism is not a denominational sub-group within the Baptist camp, but is rather a broad type that transcends different associations or fellowships. It is in that sense comparable to fundamentalism, landmarkism, etc. I use this term from time to time and have been asked what it means.
While studying Baptist groups, I first ran across the term "primitivism" in the works of Albert Wardin (Baptist Atlas and Baptists Around the World). In classifying Baptists, Wardin identifies a number of groups as Primitivists. Primitive Baptists are probably the largest group of Baptists that would be considered Primitivists, but primitivism is not synonymous with Primitive Baptists. A number of Baptist groups are considered primitivists, especially the Old Regular Baptists, Primitive Baptists, Regular Baptists, United Baptists, "Two-Seed" Baptists, the "Duck River" Baptists, some old-time Missionary Baptists, and a few Free Will Baptists.
Persons hearing the terminology "Primitivist" or "Primitive" Baptist may think of crude or backward. The idea is really "original." When people started using the term "Primitive Baptist", they meant that they believed "Primitive" Baptist was the strain of Baptist that best represented what Baptists originally were. Lemuel Potter (Old School) and W. P. Throgmorton (Missionary) once held a debate called "Who are the Primitive Baptists?" Each held his own group to be the "primitive"/original Baptists.
Back to the original question - What is primitivism? My dictionary says, "belief in the superiority of a simple way of life close to nature." Translated in the religious realm this means a preference for the "simpler" times of the "primitive" (New Testament) church. Put another way, it is the desire of primitivism to recreate and live New Testament Christianity. Martin Marty calls it "the dream of restoration of a purer order." Primitivism in motivation is related to the restorationism of Alexander Campbell & others. One major different between primitivistic Baptists and Campbell would be that these Baptists believe that they have constantly been recreating primitive Christianity, whereas Campbell believed that it had disappeared and needed "restoration". "An Anabaptist, (Michael) Servetus believed what has always been basic to restorationism: that the true, apostolic church went into apostasy, that all existing churches are false, and that the only way to have the true church again is by a restoration of primitive Christianity. This is also known as primitivism, which implies that the New Testament provides a detailed pattern for the church, so that in any age the true church can be reproduced by faithful adherence to the New Testament mode...[Leroy Garrett in Encyclopedia of Religion in the South, p. 641]." The above paragraph was written by a Restorationist, so it reflects more of the idea of restoration, but it still presents the basic idea of primitivism - that the New Testament provides the pattern for the continual faithful reproduction of the church. Don't all Baptists believe this? Probably most would say so; but they do not mean it the same way as the small subsection considered "primitivists."
I will try to give a few examples of how primitivism reveals itself among Baptists. The following information is from Local Baptists, Local Politics: Churches and Communities in the Middle and Uplands South by Clifford A. Grammich, Jr. In his research on six groups of primitivistic sects (Central, Duck River, Old Missionary, Old Regular, Eastern District Primitive, and United Baptists), Grammich compiled a grouping of "common characteristics" among these churches (pp. 93-111). These common characteristics should not be seen as synonymous with primitivism, but rather the way primitivism worked itself out among these particular churches.
If primitivism is an attempt to recreate the purer order of the New Testament, the following ways are seen as part of how churches in these six groups try to recreate that order. Grammich says, "What becomes evident is that this religion is a religion of the common people, and that the common people shape it...(p. 93).
1. Belief in the King James Bible as the unerring Word of God.
2. Emphasis on Ancient Origins of Their "True" Faith.
3. Belief in Salvation somewhere between Predestination and Free Will. [Grammich's study did not include the Regular or Absolute Primitive Baptists]
4. Emphasis on Personal, Experiential Knowledge of Salvation.
5. Non-professional Clergy without Formal Religious Education.
6. Opposition to Missions. [some would argue they only oppose "mission methods"]
7. Simple, Egalitarian Style of Worship. [examples include extemporaneous sermons, extemporaneous prayers, shouting, traditional hymns usually without instruments, outdoor baptisms, communion and footwashing]
8. Weak Central Authorities.
9. Traditional Sex Roles.
10. Rural Origins and Membership.
11. Stable Growth at Home but Losses through Migration.
Grammich notes parallels on the KJV issue with fundamentalists (point 1), but also quotes Deborah McCauley saying, "their preference in biblical literature differs profoundly from a preponderance of evangelical fundamentalism in particular...they accept ambiguity -- running deep and broad -- as an indisputable fact of life. They do not feel driven to resolve it in their preaching with semantically fancy footwork that artificially overcomes ambiguity by forcing all the pieces to fit together neatly...(p.95)." Though he also sees a common theme with landmarkism in point 2, Grammich knows of no formal connection between the two. It is my opinion that the commonalities between primitivism and landmarkism (with some Baptists sharing both ideas) helped landmarkism grow its base. The vast majority of modern landmark Baptists are no longer considered primitivists.
If you believe that the New Testament provides a detailed pattern for the church, that can be reproduced by faithful adherence to the New Testament....
....you just might be a "Primitivist".